Remote Sensing of Environment 98 (2005) 201 – 211
www.elsevier.com/locate/rse
Leaf BRDF measurements and model for specular and
diffuse components differentiation
Laurent Bousquet a,c,*, Sophie Lachérade a,d, Stéphane Jacquemoud a,c, Ismaël Moya b
a
Université Paris 7 - Denis Diderot, Laboratoire Environnement et Développement, CP 7071, 2 place Jussieu, 75251 Paris Cedex 5, France
b
Centre National de la Recherche Scientifique, Laboratoire pour l’Utilisation du Rayonnement Electromagnétique,
Université de Paris-Sud, 91405 Orsay Cedex, France
c
Institut de Physique du Globe de Paris, Géodésie et Gravimétrie, CP 89, 4 place Jussieu, 75252 Paris Cedex 5, France
d
Office National d’Etudes et de Recherches Aérospatiales, Département d’Optique Théorique et Appliquée, 2 avenue Edouard Belin,
31055 Toulouse Cedex 4, France
Received 12 April 2005; received in revised form 11 July 2005; accepted 12 July 2005
Abstract
This paper aims to link the spectral and directional variations of the leaf Bidirectional Reflectance Distribution Function (BRDF) by
differentiating specular and diffuse components. To do this, BRDF of laurel (Prunus laurocesarus), European beech (Fagus silvatica) and
hazel (Corylus avellana) leaves were measured at 400 wavelengths evenly spaced over the visible (VIS) and near-infrared (NIR) domains
(480 – 880 nm) and at 400 source-leaf-sensor configurations. Measurement analysis suggested a spectral invariance of the specular
component, the directional shape of which was mainly driven by leaf surface roughness. A three-parameter physically based model was fitted
on the BRDF at each wavelength, confirming the spectral invariance of the specular component in the VIS, followed by a slight deterioration
in the NIR. Due to this component, the amount of reflected light which did not penetrate into the leaf, could be considered as significant at
wavelengths of chlorophyll absorption. Finally, by introducing the PROSPECT model, we proposed a five-parameter model to simulate leaf
spectral and bidirectional reflectance in the VIS – NIR.
D 2005 Elsevier Inc. All rights reserved.
Keywords: Leaf optics; BRDF; Photogoniometer; Model
1. Introduction
Plant leaves are the main organs intercepting the photosynthetic active radiation (PAR) from 400 to 800 nm. Their
optical properties vary with the wavelength and the measurement configuration: the spectral and directional distributions
of incoming and outgoing light can be exploited to get
information about leaf biochemistry and anatomy. Most
papers have focused on the leaf spectral reflectance and
transmittance in connection with their chlorophyll, water,
cellulose, nitrogen, etc., contents. From such measurements,
* Corresponding author. Université Paris 7 - Denis Diderot, Laboratoire
Environnement et Développement, CP 7071, 2 place Jussieu, 75251 Paris
Cedex 5, France.
E-mail address: lbousque@ccr.jussieu.fr (L. Bousquet).
0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.rse.2005.07.005
Allen et al. (1969) estimated the effective refractive index of
corn by inverting a plate model based on geometric optics.
Jacquemoud and Baret (1990) further developed the PROSPECT model, which led to precise water, chlorophyll and dry
matter content estimation for various kinds of leaves.
Woolley (1971) was among the first to take interest in the
spatial distribution of reflected light on philodendron, maize
and soybean leaves: he distinguished diffuse from specular
components and showed that the latter was significant
contrary to the usual assumptions in most canopy reflectance
models. Breece and Holmes (1971) scanned nineteen narrow
wavebands, observing that the specular component was
relatively more important in strong absorption domains.
Finally Brakke et al. (1989) related the characteristics of those
two components to leaf anatomy but their measurements were
restricted to a single wavelength.
202
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Previous studies on leaf optical properties emphasized
that the distinction between specular and diffuse reflection
was required to improve the link between biophysical
parameters and remote sensing data. It is therefore relevant
to separate these two components in plant leaf reflection
because they carry different information. On the one hand,
the diffuse component results from multiple scattering of
light within the leaf. Its angular distribution is quite
isotropic and thus does not carry any exploitable information while its spectral variation depends on leaf biochemistry and thus can be used to estimate the amount of the leaf
constituents. On the other hand, the specular component
results from the single regular scattering at the leaf surface.
It consequently depends on surface biophysical properties.
Its magnitude and angular distribution should permit the
estimation of the refractive index or the roughness of the
epidermis/cuticle layer. Conversely, its spectral variation
should not be or very little affected by constituents like
chlorophyll in the VIS.
To separate specular reflectance from diffuse reflectance,
polarization measurements are classically used. This is
because surface scattering polarizes the incident light, while
the multiple scattering within the leaf mesophyll, created by
the many discontinuities between the air spaces and the cell
walls, does not. Vanderbilt and Grant (1986) developed an
optical device measuring polarization effects for this
purpose. With this technique, Brakke (1994) showed that
the specular component was almost the same in the VIS –
NIR whereas the diffuse component decreased in the VIS.
The directional repartition of the reflected light as a function
of wavelength should confirm this experimental result but it
has not been previously studied because appropriate datasets
were lacking.
Since BRDF are measured, models have been developed
to fit them. Ward (1992) and Brakke et al. (1989) proposed
simple equations leading to the estimation of empirical
parameters. To go further in the interpretation of the signal,
physically based models are required. The concepts of
Bidirectional Reflectance and Transmittance Distribution
Functions (BRDF and BTDF) detailed in Nicodemus et al.
(1977) capture the spectral and directional variations of
optical properties. It is now widely used in the remote
sensing community and also in the field of computergenerated pictures. Most surface BRDF models with
physical input parameters are seen as the sum of a specular
and a diffuse component. The simplest way to describe the
diffuse component is the Lambert model which assumes that
light is isotropically reflected, which, of course, is an
idealistic behaviour. Torrance and Sparrow (1967) laid the
foundations for more realistic surface BRDF models. They
treated the surface as small facets, however much larger than
the wavelength and applied the laws of geometric optics to
derive the corresponding BRDF. Cook and Torrance (1981)
and Oren and Nayar (1995) extended this work with
accurate expressions for the specular and diffuse components. Govaerts et al. (1996) and Baranoski and Rokne
(2004) built models for use with ray tracing techniques.
High computing requirements however have prevented
inverting such models.
This paper aims to link the spectral and directional
variations of leaf BRDF by differentiating specular and
diffuse components. To do this we measured leaf BRDF at
400 wavelengths evenly spaced over the VIS – NIR from
480 to 880 nm and at 400 source-leaf-sensor configurations.
We first analyzed both specular and diffuse components as
they appeared in our measurements and tested the influence
of leaf surface roughness on the BRDF pattern. Then we
modeled the observed BRDF as the sum of a diffuse and a
specular component to study their spectral variation and we
estimated the amount of light that really penetrated into the
leaf. Finally we gave an interesting perspective to such a
model for leaf surface properties estimation and leaf BRDF
modeling with a minimum number of parameters.
2. BRDF measurements
This section presents the main physical quantities used in
this study and describes the device and campaign for leaf
BRDF measurements.
2.1. Definitions
The Bidirectional Reflectance Distribution Function
(BRDF) characterizes the bidirectional reflectance properties of an object. It is defined as the ratio of its radiance R to
the irradiance I:
BRDFðk; hs ; us ; hv ; uv Þ ¼
Rðk; hs ; us ; hv ; uv Þ
I ðk; hs ; us Þ
ð1Þ
where all the notations and units are specified in Table 1.
The azimuth illumination angle u s is conventionally equal
to zero and will not be mentioned. Note that the Bidirectional Reflectance Factor (BRF) also commonly used in
remote sensing equals k times the BRDF. An important
related quantity is the Directional Hemispheric Reflectance
Factor (DHRF) defined as:
Z 2PZ P=2
DHRFðk; hs Þ¼
BRDFðk;hs ;hv ;uv Þcoshv sinhv dhv duv :
0
0
ð2Þ
2.2. Measurement device
Measurements were performed with a spectro-photogoniometer developed by the Institut National de la
Recherche Agronomique (Combes, 2002), the University
of Paris 7, and the LURE/CNRS. This device which is fully
described in a forthcoming paper was specifically designed
for leaf BRDF/BTDF measurements but has also been used
for BRDF measurements of man-made, opaque materials
like slates. We used a halogen light source producing
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Table 1
Notations
Symbol
with a 1 nm step. Accurate derivation of measurement error
has not been driven.
Quantity
Unit (symbol)
None
None
None
None
Nanometer (nm)
Degree (-)
a
R
Illumination direction
Viewing direction
Normal to the sample
Normal to the facet
Wavelength
Illumination (solar) zenith angle
(in spherical coordinates)
Illumination (solar)
azimuth angle
(in spherical coordinates)
Viewing zenith angle
(in spherical coordinates)
Viewing azimuth angle
(in spherical coordinates)
Half of the phaseYangle
Y
between L and V
Y
Y
Angle between N and H
Radiance
I
Irradiance
Y
L
Y
V
Y
N
Y
H
k
hs
us
hv
uv
ha
203
BRDF/BTDF Bidirectional
reflectance/transmittance
distribution function
DHRF
Directional hemispherical
reflectance factor
dX
Solid angle
kL
Lambert parameter of the
BRDF model
n
Refractive index
r
Leaf surface roughness
parameter
N
Leaf structure parameter
C ab
Leaf chlorophyll content
Cm
Leaf dry matter content
Degree (-)
Degree (-)
Degree (-)
Degree (-)
Degree (-)
Watt per square
meter per steradian
(W m 2 sr 1)
Watt per square
meter (W m 2)
Unit per
steradian (sr 1)
None
Steradian (sr)
None
None
None
None
Ag cm 2
g cm 2
unpolarized radiation in the VIS – NIR, which was carried to
an illumination arc by an optical fiber. The zenith
illumination angle could be set to 8-, 21-, 41-, and 60-.
The sample holders were designed for leaves and reflectance
standards of about 30 mm wide. Seven detectors in different
viewing directions were arranged along a fixed reception
arc. By moving together the illumination arc and the sample
holder, one could obtain 98 different observation directions.
The radiometric measurements ranged from 480 to 880 nm
2.3. Measurement campaign
Measurements were made during spring 2003 on leaf
species listed in Table 2. As surface effects are thought to be
of great importance for BRDF pattern, species were selected
to display various kinds of surface structure. Cherry laurel
with a thick smooth cuticle on the adaxial face was very
bright to the naked eye. In the opposite extreme, hazel
presented a diffuse aspect because of its hairy surface.
European beech, one of the most widespread tree species in
Europe, was intermediate in leaf characteristics. The other
leaves were selected for their economic interest like maple, a
high-value ornamental plant, or like green bean, because it
has been the subject of experimental measurements in our
laboratories. Brakke et al. (1989) has shown differences in the
BRDF of adaxial and abaxial faces. Measurements over both
faces of several leaf samples of each species have been made
to address this difference and the intra-species variability. A
full BRDF acquisition corresponding to 4 illumination
directions, 98 viewing directions, and 400 wavelengths took
less than an hour after the leaf was removed from the plant.
We assumed a minimal pigment and anatomy degradation,
i.e. unchanged leaf optical properties in the VIS – NIR.
The size of the lit and viewed area of the leaf may
influence the measurement of the leaf BRDF. Regardless of
illumination and viewing directions, we set the observed
area of the leaf to be smaller than the lit one. As we wished
to avoid major veins on the leaf, it was necessary for the lit
area to be smaller than a few square centimeters. However,
it also needed to be large enough to average the properties of
the mesh constituted by the leaf areolaes, which are the
spaces enclosed by anastomosing veinlets. Wylie (1943)
measured the area of areolae in more than ten species and
found an average area of 0.06 mm2. An observed area one
hundred times greater, i.e., 6 mm2, thus guarantees sufficient
averaging of the optical properties for a mesh of this size.
The lit and viewed areas of the leaf were set to satisfy these
constraints. Mechanical defects affected the localization of
the viewed area at grazing angles and caused a signal loss
beyond h v = 70- so that the corresponding BRDF values
were not accounted for in this study although they were
Table 2
Description of the dataset
Sample
Description
Type of measurement
Hazel (Corylus avellana)
Cherry laurel (Prunus laurocesarus), young leaf
Cherry laurel (Prunus laurocerasus), old leaf
European beech (Fagus silvatica)
Maple (Acer pseudoplatanus), young leaf
Maple (Acer pseudoplatanus), old leaf
Maple (Acer pseudoplatanus), old leaf
Green bean (Phaseolus vulgaris var. contender)
Downy and undulating
Clear green, flexible leave
Dark green, rigid
Very undulating
Bright and undulating
Mat and flat
Green adaxial and purple abaxial faces
Slightly undulating
Adaxial
Adaxial
Adaxial
Adaxial
Adaxial
Adaxial
Adaxial
Adaxial
and abaxial
and abaxial
and abaxial
and abaxial
and abaxial
and abaxial
and abaxial
BRDF
BRDF
BRDF
BRDF
BRDF
BRDF
BRDF
BRDF
204
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
should permit the localization of the specular peak and the
400 wavelengths, correspondingly, the study of its spectral
composition. Fig. 1 shows the BRDF of laurel at 550, 670,
and 780 nm. The BRDF are plotted for a given wavelength
(E) and a given illumination direction (h s) in polar coordinates (r, h), respectively, equal to (h v, u v). Incident direction is represented by a star. Thus one plot shows the variation
of the BRDF over the whole hemisphere. Directions of
experimental data acquisition are marked by dots. The other
values have been interpolated for this representation. The first
waveband corresponds to the maximum leaf reflection in the
visible domain (green), the second one to a minimum
reflection (red), and the third one lies in the near-infrared
domain where reflection reaches a high plateau (due to
minimum absorption). The incidence angle h s is set to 60- to
enhance the specular reflection at all wavelengths.
The BRDF pattern consists of a thin high peak in the
specular direction and a uniform background in all other
viewing directions. The peak maximum is about 1.2 sr 1
and may vary up to 10% with wavelength. The intensity of
the background is smaller than 0.1 sr 1 in the VIS and
about 0.2 sr 1 in the NIR. The peak in the BRDF is thus
identified as almost pure specular reflection. In comparison,
although diffuse reflection appears very low, it becomes
predominant once integrated over the whole hemisphere.
Indeed, the specular peak reaches high intensities but
remains confined within a small solid angle. The laurel
DHRF (Eq. (2)) which has been evaluated for h s = 60- by
numerical summation is about 0.1 in the red, 0.2 in the
green, and 0.5 in the near-infrared. If the contribution of
plotted. Effects of the geometry of the incident and reflected
light beams have not been studied.
Measuring leaf BRDF, one has to account for their
undulating shape and surface features that are responsible
for several roughness scales. The latter must be compared
with the length of the observed surface, about 1 cm in the
present work. When below this the roughness is intrinsic to
the sample and may be modeled as described in the
following section. However it may tilt the average plane
of the observed surface in the sample holder. As a result the
observed specular reflection may not be in the expected
direction. We selected samples with specular peaks in the
principal plane defined as the plane of the incident light
beam and the normal to the sample holder.
3. Analysis of measured BRDF
In this section we aim to distinguish specular from
diffuse reflection patterns directly in the measured BRDF
and to study the impact of various leaf surface roughnesses
on the directional shape of the BRDF.
3.1. Discrimination of specular and diffuse reflections in the
laurel BRDF
Because of a thick smooth cuticle and high chlorophyll
content, the laurel leaf is the most suitable for the observation
of a strong white specular peak on a green diffuse background
caused by chlorophyll absorption. The 98 viewing directions
Wavelength (nm)
0.6
0.5
DHRF
0.4
550nm
0.3
780nm
670nm
0.2
0.1
0
500
550
600
650
90o
135o
750
700
800
90o
135o
45o
850
90o
135o
45o
1.2
45o
1
0.8
o
180o
0
o
180o
0
o
180o
0
0.6
0.4
225o
315o
270o
225o
315o
270o
225o
315o
0.2
270o
Fig. 1. Laurel DHRF (top) and BRDF (bottom) calculated for h s = 60- at 550 (left), 670 (middle), and 780 nm (right). The bar scale is the same for the
three plots.
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Laurel
Beech
Hazel
90o
90o
90o
205
0.06
135o
135o
45o
135o
45o
45o
0.05
0.04
0o 180o
180o
0o 180o
0o
0.03
0.02
315o
225o
270o
315o
225o
315o
225o
270o
270o
0.01
0
Fig. 2. BRDF of adaxial leaf faces of laurel (left), European beech (middle), and hazel (right) for h s = 21- and k = 680 nm. The bar scale is the same for the
three plots.
specular reflection to the DHRF is constant, it must be less
than 0.1 DHRF unit. This could still represent the half or
more of the reflected light in the visible domain. In the next
section, the use of a BRDF model will enable us to
accurately quantify this contribution.
3.2. Influence of surface roughness
Differences in BRDF patterns are thought to come from
specular reflection. For wavelengths of strong absorption, for
instance 680 nm where chlorophyll is at full absorption,
specular reflection is highlighted when compared to diffuse
reflection, as previously noticed by Walter-Shea et al. (1989).
The experimental BRDF of the three leaf species, beech,
laurel, and hazel, are presented in Fig. 2 to illustrate different
BRDF magnitudes and patterns. All leaves showed forward
scattering whereas no backscattering was observed. With its
thick cuticle creating a very smooth surface on the adaxial
face, laurel displayed a thin high BRDF peak localized in the
specular direction. Hazel was much more Lambertian, with a
maximum reflectance measured at very high viewing angles.
This may be due to its hairy surface and undulated shape.
Finally, beech showed an intermediate BRDF pattern with a
lower reflectance and peak localized over a larger area
between 20- and 40-. As noticed by Woolley (1971) and
Walter-Shea et al. (1989), the maxima of BRDF may appear
at a greater angle than for a mirror-like reflection. This effect
which is due to leaf roughness (Torrance and Sparrow, 1967)
tends to vanish when the latter decreases. As the zenith
illumination angle increases, the three samples become more
specular and the BRDF peak becomes narrower and higher.
For a 60- illumination angle, BRDF maxima are 1.1 sr 1 for
laurel, 0.29 sr 1 for beech and 0.14 sr 1 for hazel. The
differences between the three samples remain such that
differentiation based upon their BRDF shape is possible.
4. Modeling of leaf BRDF and applications
Because they contain both a spectral and a bidirectional
dimension, our BRDF measurements allowed us to identify
specular and diffuse reflection components and to look at
surface roughness effects. In this section we propose a
BRDF model defined as the sum of diffuse and specular
components and we test its ability to fit the experimental
measurements. It will permit to assess the spectral
invariance of the specular component and to evaluate the
amount of reflected light that did not penetrate into the leaf.
We also investigate perspectives for the estimation of leaf
surface properties and propose a simple way to represent
leaf BRDF in the VIS – NIR with only five parameters.
4.1. Derivation of a geometric optics BRDF model
The BRDF is assumed to be the sum of the diffuse and
specular components, namely BRDFdiff and BRDFspec:
BRDF ¼ BRDFdiff þ BRDFspec :
ð3Þ
We wish to derive a simple and general expression of leaf
BRDF that can be used for model inversion or for plant
canopy reflectance simulations. The diffuse component
represents the fraction of reflected light which is not single
specular reflection at the leaf surface. We assume Lambertian behaviour and a strong dependence on wavelength so
that BRDFdiff may be written:
BRDFdiff ðk; hs ; hv ; uv Þ ¼
k L ð kÞ
k
ð4Þ
where 1 / k is the BRDF of a perfect Lambertian scatterer
and k L(k) is the Lambert coefficient. Note that the diffuse
component does not vary with the incidence angle. To
model the shape of the specular component, one needs to
consider the leaf surface as a rough interface between air
and leaf material. A recurrent modeling approach for rough
surfaces assumes that they are composed of a multitude of
facets. Among the last ones, some reflect light specularly
Y
Y
from the illumination direction L to the viewing direction V
(Fig. 3). Torrance and Sparrow (1967), Cook and Torrance
(1981), and Oren and Nayar (1995) derived various BRDF
expressions based on this approach. Consider a plane
surface of area S illuminated by a parallel light beam. At
a smaller scale this surface is made of N f tilted mirror-like
206
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
N (leaf normal)
L (illuminating dir.)
H (facet’s normal)
α
V
(viewing dir.)
θs
θv
Facet under
consideration
The Fresnel factor F(n, h a) drives the amount of light
reflected at the boundary between air and leaf material.
The cuticle which coats the leaf epidermal cells (Juniper
and Jeffree, 1983) is assumed to be a low absorbing
medium compared to the leaf interior. Thus its absorption
can be neglected and its refractive index assumed real.
The Fresnel factor is calculated for a plane dielectric
boundary between two semi-infinite media and unpolarized light:
" #
1 g cosha 2
cosha ð g þ cosha Þ 1 2
F ðn; ha Þ¼
1þ
2 g þ cosha
cosha ð g cosha Þ þ 1
ð8Þ
Observed leaf area
Fig. 3. Notations for the main directions and angles.
facets of the same area S f. Facets are identified by the
direction of their normal (a, U). The probability to find a
facet (a, U) in the solid angle dX = sinadadU is D(a, U)dX
where the probability density function D(a, U) is normalized to unity. The area of the plane surface is linked to the
facet area by the following expression:
Z 2PZ P=2
S¼
cosaNf Dða; UÞsinadadU:
ð5Þ
0
0
We calculate the BRDF for an illumination direction
(h s, u s) and a viewing direction (h v, u v). Only facets
producing specular reflection between these two directions
are accounted for. The amount of reflected light by a single
facet is given by the Fresnel factor F(n, h a) which depends
on the refractive index n of leaf surface material and the
angle of incidence h a between the normal to the facet and
the illumination direction. Oren and Nayar (1995) detailed
the geometrical effects of multiple specular reflections and
mutual facet masking or shadowing which led to several
conditional expressions. For simplicity’s sake we used the
approach of Cook and Torrance (1981) which assumes a
multiplying geometrical attenuation factor G depending
only on the illumination and viewing directions. This yields
to the following expression (readers are invited to refer to
Torrance and Sparrow (1967) for details):
with g 2 = n 2 + cos2h a 1. When absorption cannot be
neglected, this factor is expressed as a function of the
real and imaginary parts of the complex refractive index
of the medium.
The probability density function D(a, U) used in
Torrance and Sparrow (1967) and Oren and Nayar (1995)
is a Gaussian distribution of the variable a leading to
difficulties in evaluation of integral forms. In order to
represent a wide panel of surfaces and to make the integral
of S calculable, we used the expression of D proposed by
Cook and Torrance (1981) and which depends on a
roughness parameter r:
c
tan2 a
Dða; U; rÞ ¼ 2 4 exp 2
:
r cos a
r
The normalization factor c is not present in their work
but it cancels in the final expression of BRDFspec. Note that
the azimuth angle U does not affect the probability to find a
facet (a, U). This expression permits the calculation of the
factor (S fN) / S in Eq. (6) yielding to an expression
independent of the roughness parameter r.
The final BRDF expression for BRDFspec is:
BRDFspec ðn; r; hs ; hv ; uv Þ ¼
F ðn; ha ÞGðhs ; hv ; uv Þ
2k2 coshs coshv
2
BRDF spec ðk; hs ; hv ; Uv Þ ¼
F ðn; ha ÞDða; UÞGðhs ; hv ; Uv Þ
4coshs coshv
Sf N f
ð6Þ
S
where:
Gðhs ; hv ; uv Þ ¼ minð1; E1 ; E2 Þ
ð7Þ
v
s
with E1 ¼ 2cosacosh
and E2 ¼ 2cosacosh
cosha
cosha . The angles h a and a
s þcoshv
are derived from basic geometry as cosa ¼ cosh2cosh
and
a
cos 2h a = cosh scosh v + sinh ssinh vcosu v.
ð9Þ
2
etan a=r
:
r2 cos4 a
ð10Þ
Using this expression for leaves, one should keep in
mind that it is just a simplification since other leaf
surface features like trichomes of hairy leaves (Fuhrer et
al., 2004) may involve other optical phenomena like
diffraction. In the absence of such surface features, the
facets of the BRDF model may correspond to the leaf
areolae defined as the spaces enclosed by anastomosing
veinlets.
The simulated BRDF depends on the refractive index n
via the Frenel factor, the behaviour of which is well-
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Laurel
Beech
1
Hazel
1
1
1.8
0.8
1.6
n
1.4
1.2
0.6
0.2
0
1.6
0.8
1.6
0.6
1.4
1.2
0.6
1.4
1.2
600
700
1
1
σ
500
0.4
0.4
0.2
0.2
0
800
500
Wavelength (nm)
600
700
0
800
800
0.25
Modeled
0.3
Modeled
700
0.3
1
Modeled
600
Wavelength (nm)
0.4
0.6
500
Wavelength (nm)
1.2
0.8
1.8
1.8
0.8
1
kL
0.4
207
0.2
0.4
0.2
0.15
0.1
0.1
0.2
0
0.05
0
0.5
1
0
0
0.1
Measured
0.2
0.3
0
0.4
0
0.1
Measured
0.2
0.3
Measured
Fig. 4. Three-parameter model inversion at each wavelength for laurel (left), beech (middle), and hazel (right). Top: parameter values as a function of
wavelength. Scale for k L and r on the left, for n on the right. Bottom: measured vs modeled BRDF.
known, and on the roughness parameter via the probability
density function D. Provided that the roughness parameter
r is smaller than 0.7, the probability to find a facet with
the tilt a decreases when a increases. For a given n,
r < 0.1 leads to a thin high specular peak, r å 0.3 to a
much wider and weaker peak, and r > 0.5 to a forward
scattering rather than a specular peak. To study the effects
of n and r on the reflected light over the whole
hemisphere we derived the DHRF due to BRDFspec,
namely DHRFspec. For n equal to 1.4 and r increasing
from 0.1 to 0.5, DHRFspec remains unchanged for
incidence angles lower than 30- and decreases with r
especially as the incidence angle is large. For r = 0.25 and
n increasing from 1.2 to 1.8, DHRFspec does not change
for large incidence angles and increases with n especially
at small incidence angles. Thus increasing the roughness
parameter r tends to reduce DHRFspec at large incidence
angles while increasing the refractive index n tends to
increase DHRFspec at small incidence angles.
4.2. Inversion of the model for each wavelength of the
measured BRDF
The BRDF model has three input parameters (k L, n,
and r) and we experimentally measured the shape of the
BRDF of several plant leaves at 400 wavelengths. Thus
we can retrieve these parameters at each wavelength
separately by minimizing the merit function v 2 defined
as:
v2 ð kÞ ¼
X
ðBRDFmeasured BRDFmodeled Þ2 :
ð11Þ
hs ;hv ;uv
Because data acquired at viewing zenith angles higher
than 70- invite criticism as above-mentioned, only 65
viewing directions of the 98 measured were used, which
represent 260 reflectances for each sample at each of the
400 wavelengths. The optimization has been constrained
by fixing the lower and upper parameter bounds. For one
inversion, the initial parameter set is the same for all the
samples and all the wavelengths. Several inversions
performed with various initial parameter sets led to
similar results. Results are presented in Fig. 4 for the
parameter set shown in Table 3. Measured vs modeled
BRDF values are in good agreement. Fig. 5 shows the
measured and modeled BRDF at wavelengths of mini-
Table 3
Parameter sets for model inversion
Lower bound
Upper bound
Initial value
kL
n
r
0.01
0.99
0.3
1.1
5
1.47
0.01
1
0.3
208
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Laurel at 672 nm
Beech at 669 nm
90o
90o
0.18
o
o
135
45
90o
o
0.16
Hazel at 664 nm
135
45
0.1
o
0.06
o
45o
135
0.05
0.14
0.08
0.12
0o
180o
0.04
0.1
0.08
180
0o
o
0.04
315o
90
0
180
o
90
90
0.18
135o
0.16
0
270o
o
45o
0.01
315o
225o
0
270o
o
0.06
0.1
45o
135o
45o
0.05
0.14
0.08
0.12
180
o
0
o
0.04
0.1
0.08
180
0
o
o
0.04
315o
o
0
180
o
0
270o
0.01
315o
225o
315o
225o
0.03
0.02
0.02
0.02
0
270o
0.06
0.04
0.06
225o
0.03
0.02
315o
225o
0
135o
o
0.02
0.02
270o
o
0.04
0.06
225o
0.06
0
270o
Fig. 5. Measured (top) and modeled (bottom) BRDF for h s = 41- at wavelengths of minimum reflection.
variations ((maxmin) / mean) of n are about 2% for
laurel, 5% for beech, and 10% for hazel. r varies by
about 8%, 7%, and 9%, respectively. These variations
increase in the NIR, almost reaching 25% for the
refractive index of hazel. Note that the spectral variation
of n in the NIR has the same pattern for beech and hazel.
The spectral invariance of the specular component can
consequently be considered as a good approximation in
the VIS that deteriorates in the NIR.
mum reflection. They reveal very similar directional
shapes. This proves the ability of the model to fit the
directional variations of the reflected light that did not
penetrate into the leaf.
4.3. Spectral invariance of the specular component
The parameters n and r vary quite slowy over the
whole measured spectrum compared to k L. In the VIS, the
Laurel
Beech
0.5
DHRF
DHRF
0.4
0.3
0.5
0.5
0.4
0.4
DHRF
diff
spec 8o
spec 21o
spec 41o
spec 60o
Hazel
0.3
0.3
0.2
0.2
0.2
0.15
0.15
0.15
0.1
0.1
0.1
0.05
0.05
0.05
0
500
600
700
800
Wavelength (nm)
0
500
600
700
800
Wavelength (nm)
0
500
600
700
800
Wavelength (nm)
Fig. 6. Estimated diffuse and specular contributions to the DHRF for laurel (left), beech (middle), and hazel (right). Specular contribution is plotted for
illumination angles h s = 8-, 21-, 41-, and 60- (diffuse contribution is the same whatever the illumination angle).
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Table 4
Mean leaf surface characteristics estimated in the 480 – 880 nm range
Laurel
Beech
Hazel
4.5. Perspective for the estimation of leaf surface
properties
Refractive index n
Roughness parameter r
1.22
1.56
1.68
0.078
0.29
0.46
Although plant cuticle has been studied in detail by
Martin and Juniper (1970), Cutler et al. (1982) or Kerstiens
(1996), its optical or roughness properties have barely been
measured. The mean values of the retrieved cuticle
refractive index and roughness parameter from 480 to
880 nm are listed in Table 4. The roughness parameter is
minimum (r ¨ 0.078) for laurel which has a thick cuticle,
maximum (r ¨ 0.46) for hazel which has hairy faces, and
intermediate (r ¨ 0.29) for beech which has an intermediate surface structure. This result is consistent with our
observations on fresh leaf materials. To the best of our
knowledge, measured values for roughness of leaf surfaces
have not been published so far. The refractive index
follows the opposite variation: it is higher for hazel than
for laurel. This can be explained by the high reflectance of
hairy leaf even at low incidence angles. Hairs reflect light
that has not interacted with the leaf interior and increase the
apparent refractive index. Allen et al. (1969) give 1.47 for
the refractive index of carnauba wax, a substance obtained
from the leaf surface of Capernicia cerifera and Woolley
(1975) proposes 1.48 for the living hairs of soybean leaves.
In comparison the 1.22 value found for laurel is lower and
those found for beech (1.56) and hazel (1.68) are higher.
Various cuticle structures associated with an increase due to
the presence of hair may explain such differences.
4.4. Evaluation of the amount of light that did not penetrate
into the leaf
The retrieved model parameters are then used to estimate
the diffuse and specular contributions to the DHRF at each
wavelength:
DHRFðhs ; kÞ ¼ DHRFdiff ðhs ; kÞ þ DHRFspec ðhs ; kÞ
ð12Þ
with:
DHRFdiff ðhs ; kÞ
Z 2PZ P=2
¼
BRDFdiff ðk; hs ; hv ; uv Þcoshv sinhv dhv duv
0
0
¼ kL ðkÞ
ð13Þ
DHRFspec ðhs ; kÞ
Z 2PZ P=2
¼
BRDFspec ðnðkÞ; rðkÞ; hs ; hv ; uv Þ
0
4.6. Perspective for a five-parameter leaf optical properties
model using PROSPECT
0
ð14Þ
coshv sinhv dhv duv :
In the above, the BRDF model requires three input
parameters (k L, n, and r) at each wavelength, i.e., a total
of 3 400 = 1200 parameters to simulate the full spectral
and directional leaf optical properties in the VIS – NIR.
This is neither convenient nor portable. We aim to reduce
this number to only five. On the one hand, the refractive
index n and roughness parameter r have been shown to be
almost wavelength independent in the VIS –NIR so that
they can be replaced by their mean values. On the other
DHRFspec was numerically computed with a relative
error below 10 4. Fig. 6 shows both contributions for
the four incidence angles h s. The specular contribution
varies very slowly with the wavelength, whatever the
leaf and the incidence angle. It is almost the same for
h s = 8-, 21- and 41- and double at h s = 60-. It can be
higher than the diffuse one for wavelengths of strong
absorption.
Laurel
0.4
0.3
0.2
0.1
0
Hazel
0.6
0.6
0.5
0.5
Reflectance
Reflectance
0.5
Beech
kL + DHRFs(0o)
PROSPECT
Reflectance
0.6
209
0.4
0.3
0.2
0.1
500
600
700
800
Wavelength (nm)
900
0
0.4
0.3
0.2
0.1
500
600
700
800
Wavelength (nm)
900
0
500
600
700
800
900
Wavelength (nm)
Fig. 7. DHRF (k, 0-) simulated with the BRDF model (solid line) and fitted with the PROSPECT model (dashed line).
210
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
Table 5
Root mean square error (RMSE) between measured and modeled leaf
BRDF
Laurel
Beech
Hazel
RMSE (k L(k), n(k), r(k))
RMSE (n, r, N, C ab, C m)
1.51 10 2
1.12 10 2
0.90 10 2
1.70 10 2
1.17 10 2
1.01 10 2
by 65 viewing directions by 400 wavelengths. The slight
increase of the RMSE proves the effectiveness of our
approach consisting of coupling PROSPECT with the
BRDF model to simulate both the spectral and bidirectional
reflectance of plant leaves.
5. Conclusion
hand, the Lambert parameter k L(k) which is strongly
correlated with the leaf DHRF(k) can be related to the
PROSPECT model. The latter is used to simulate leaf
hemispherical reflectance and/or transmittance and
accounts for both specular and diffuse reflections, assuming that the illumination direction is normal to the leaf
blade. Thus the reflectance R prospect simulated by PROSPECT should be equivalent to DHRF (k, h s = 0-). The
parameters required to run it in the VIS –NIR are the leaf
structure parameter N (which ranges from 1 to 1.5 for
monocots and from 1.5 to 2.5 for dicots), the chlorophyll
a + b content C ab (Ag cm 2) and the dry matter content C m
(g cm 2). This yields to:
Rprospect ð N ; Cab ; Cm Þ ¼ DHRFðk; 0-Þ:
ð15Þ
By evaluating Eq. (12) for h s = 0- one has:
Rprospect ð N ; Cab ; Cm Þ ¼ DHRFdiff ðk; 0-Þ þ DHRFspec ðk; 0-Þ:
ð16Þ
From Eq. (13) DHRFdiff is equal to k L(k) for all h s.
Because n and r are approximated by their mean values,
DHRFspec is independent of the wavelength so that Eq. (16)
may be written as:
Rprospect ð N ; Cab ; Cm Þ ¼ kL ðkÞ þ DHRFspec ð0-Þ:
ð17Þ
Finally, extracting k L in Eq. (17) and substituting in Eq.
(4) leads to a new expression for the BRDF model, the
parameters of which are now wavelength independent:
BRDFðk; hs ; hv ; uv Þ
¼
Rprospect ð N ; Cab ; Cm Þ DHRFspec ðn; r; 0-Þ
p
þ BRDFspec ðn; r; hs ; hv ; uv Þ:
ð18Þ
We tested the ability of this five-parameter model to fit
our measured BRDF. Since a global inversion of Eq. (18)
led to instabilities on the retrieval of the PROSPECT
parameters, we decided to calculate the mean value of n and
r (Table 4) and then to estimate the PROSPECT parameters
by inverting Eq. (17). The fit of PROSPECT is very
satisfying as shown in Fig. 7. To compare this fiveparameter model with the previous version using 3 400
input parameters, we computed the root mean square error
(RMSE) between the measured and modeled BRDF. Values
gathered in Table 5 correspond to 4 illumination directions
Accurate leaf BRDF measurements were carried out for
laurel, beech and hazel. These three species exhibit various
BRDF shapes mainly due to the specular reflection
influenced by leaf surface characteristics. The new goniometer enabled us to record the BRDF shape as a
continuous function of the wavelength in the 480– 880 nm
range. Therefore, it was possible to show that the specular
peak in laurel BRDF was almost independent of the
wavelength. Then a BRDF model expressed as the sum of
a diffuse and a specular component was used to fit the
BRDF measurements. The parameters controlling the
specular component were found to be almost independent
of wavelength for each of the three leaf types. The model
also permitted the evaluation of the proportion of diffuse
and specular reflection at each wavelength. Finally, we
associated this model with PROSPECT and reduced the
number of parameters to only five: n (refractive index of
leaf surface material), r (surface roughness parameter), N
(leaf structure parameter) and the biochemical contents C ab
(chlorophyll) and C m (dry matter). The comparison of some
of these parameters with the leaf biophysical characteristics,
e.g., its biochemical composition or surface anatomical
structure, would be required to completely validate the
model. A laboratory experiment will soon bridge this gap.
As PROSPECT is widely used to estimate leaf
biochemical compounds from hemispherical reflectance
measurements, we wish to extend such estimates to
directional measurements. Considering the leaf blade as
an anisotropic surface instead of a Lambertian one,
especially at orientations close to the specular direction,
will change our perception of leaf optical properties, which
has many significant underlying applications in plant
physiology, computer-generated images, and vegetation
remote sensing. For instance, the model will allow plant
canopy reflectance modelers to test the validity of the
argument that leaf BRDF is a minor factor in determining
canopy reflectance.
Acknowledgements
This work was supported by the Programme National de
Télédétection Spatiale (PNTS) and by the GDR 1536
FLUOVEG (Fluorescence of Vegetation). We are grateful
to the three anonymous reviewers for their comments and
recommendations. Many thanks to Susan Ustin for reading
and correcting this paper.
L. Bousquet et al. / Remote Sensing of Environment 98 (2005) 201 – 211
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